Eigenvectors of the characteristic equation for each of the three locusts
| . | . | Eigenvectors . | . | . | . | . | . | . | . | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Locust . | Mode . | δu/ue . | Phase angle (degrees) . | δw/ue ≈δαb . | Phase angle (degrees) . | δq (rad s−1) . | Phase angle (degrees) . | δθ (rad) . | Phase angle (degrees) . | |||||||
| `R' | Oscillatory | 0.044 | −90.4 | 1.0 | −2.9 | 62 | −94.5 | 1 | 0 | |||||||
| Divergence | −0.26 | 0.64 | 5.0 | 1 | ||||||||||||
| Subsidence | 2.8 | −7.0 | −2.5 | 1 | ||||||||||||
| `G' | Oscillatory | 0.090 | 91.4 | 1.0 | 3.6 | 101 | 94.1 | 1 | 0 | |||||||
| Divergence | −0.52 | 0.46 | 5.7 | 1 | ||||||||||||
| Subsidence | 1.3 | −1.1 | −3.5 | 1 | ||||||||||||
| `B' | Oscillatory | 0.038 | 89.8 | 1.0 | 3.7 | 56 | 95.4 | 1 | 0 | |||||||
| Divergence | −0.19 | 0.62 | 6.0 | 1 | ||||||||||||
| Subsidence | −4.9 | 16.6 | −3.9 | 1 | ||||||||||||
| . | . | Eigenvectors . | . | . | . | . | . | . | . | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Locust . | Mode . | δu/ue . | Phase angle (degrees) . | δw/ue ≈δαb . | Phase angle (degrees) . | δq (rad s−1) . | Phase angle (degrees) . | δθ (rad) . | Phase angle (degrees) . | |||||||
| `R' | Oscillatory | 0.044 | −90.4 | 1.0 | −2.9 | 62 | −94.5 | 1 | 0 | |||||||
| Divergence | −0.26 | 0.64 | 5.0 | 1 | ||||||||||||
| Subsidence | 2.8 | −7.0 | −2.5 | 1 | ||||||||||||
| `G' | Oscillatory | 0.090 | 91.4 | 1.0 | 3.6 | 101 | 94.1 | 1 | 0 | |||||||
| Divergence | −0.52 | 0.46 | 5.7 | 1 | ||||||||||||
| Subsidence | 1.3 | −1.1 | −3.5 | 1 | ||||||||||||
| `B' | Oscillatory | 0.038 | 89.8 | 1.0 | 3.7 | 56 | 95.4 | 1 | 0 | |||||||
| Divergence | −0.19 | 0.62 | 6.0 | 1 | ||||||||||||
| Subsidence | −4.9 | 16.6 | −3.9 | 1 | ||||||||||||
Each row of eigenvectors corresponds to one of the roots, or eigenvalues,in Table 7 and gives the relative magnitudes and phases of the state variables that satisfy the corresponding solution to the characteristic equation.
The values of the eigenvectors are arbitrary to within a complex factor,and the eigenvectors are therefore normalised to give the pitch attitude disturbance δθ a magnitude of 1 rad and phase angle of zero.